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Dimensionality Reduction

Dimensionality Reduction​

  • Purpose
    • Avoid curse of dimensionality
    • Reduce amount of time and memory required by data mining algorithms
    • Allow data to be more easily visualized
    • May help to eliminate irrelevant features or reduce noise
  • Techniques
    • Principle Component Analysis
    • Singular Value Decomposition
    • Others: supervised and non-linear techniques

Data Dimensionaity​

  • From a theoretical point of view, increasing the number of features should lead to better performance
  • In practice, the inclusion of more features leads to worse performance (i.e., curse of dimensionality)
  • The number of training examples required increases exponentially with dimensionality

Curse of Dimensionality​

  • When dimensionality increases, data becomes increasingly sparse in the space that it occupies
  • Definitions of density and distance between points, which is critical for clustering and outlier detection, become less meaningful

Dimensionality Reduction​

  • Purpose
    • Avoid curse of dimensionality
    • Reduce amount of time and memory required by data mining algorithms
    • Allow data to be more easily visualized
    • May help to eliminate irrelevant features or reduce noise
  • Techniques
    • Principle Component Analysis
    • Single Value Decomposition
    • Others: Supervised and non-linear techniques

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https://www.datacamp.com/community/tutorials/principal-component-analysis-in-python

Feature Subset Selection​

  • Another way to reduce dimensionality of data

  • Redundant features

    • duplicate much or all of the information contained in one or more other attributes
    • Example: purchase price of a product and the amount of sales tax paid
  • Irrelevant features

    • contain no information that is useful for the data mining task at hand
    • Examples: students' ID is often irrelevant to the task of predicting students' GPA
  • Evaluate a subset of feature

  • Search for the best subset

Techniques​

Brute-force approach​

Try all possible feature subsets as input to data mining algorithm

Embedded approaches​

Feature selection occurs natually as part of the data mining algorithm

Fiter approaches​

Features are selected before data mining algorithm is run

Wrapper approaches​

Use the data mining algorithm as a black box to find best subset of attributes

Feature Creation​

  • Create new attributes that can capture the important information in a data set much more efficiently than the original attributes
  • Three general methodologies
    • Feature Extraction - domain-specific
    • Mapping data to new space
    • Feature construction - combining features

Introduction to dimensionality reduction - Blog | Hex